Apparently, your ISP is using CGN (Carrier-Grade NAT). See RFC 6264, An Incremental Carrier-Grade NAT (CGN) for IPv6 Transition. Some ISPs foolishly use RFC 1918 Private Address space for this instead of the IANA reserved address block: RFC 6598, IANA-Reserved IPv4 Prefix for Shared Address Space). This range is 100.64.0.0/10. Most ISPs don't use the range assigned by IANA for this, they just use regular RFC 1918 address space.
The RIRs have run out of IPv4 addresses to assign to the ISPs, so the ISPs are turning to CGN to assign non-public IPv4 addresses to residential customers, saving their precious pool of public IP addresses for business customers willing to pay a premium for public IPv4 addresses.
From RFC 6598:
1. Introduction
IPv4 address space is nearly exhausted. However, ISPs must
continue to support IPv4 growth until IPv6 is fully deployed. To
that end, many ISPs will deploy a Carrier-Grade NAT (CGN) device,
such as that described in [RFC6264]. Because CGNs are used on
networks where public address space is expected, and currently
available private address space causes operational issues when used
in this context, ISPs require a new IPv4 /10 address block. This
address block will be called the "Shared Address Space" and will be
used to number the interfaces that connect CGN devices to Customer
Premises Equipment (CPE).
Shared Address Space is similar to [RFC1918] private address
space in that it is not globally routable address space and can be
used by multiple pieces of equipment. However, Shared Address
Space has limitations in its use that the current [RFC1918]
private address space does not have. In particular, Shared Address
Space can only be used in Service Provider networks or on routing
equipment that is able to do address translation across router
interfaces when the addresses are identical on two different
interfaces.
This document requests the allocation of an IPv4 /10 address block
to be used as Shared Address Space. In conversations with many
ISPs, a /10 is the smallest block that will allow them to deploy
CGNs on a regional basis without requiring nested CGNs. For
instance, as described in [ISP-SHARED-ADDR], a /10 is
sufficient to service Points of Presence in the Tokyo area.
This document details the allocation of an additional special-use
IPv4 address block and updates [RFC5735].
The RFC also lists some of the problems caused by CGN:
5.2. Empirical Data
The primary motivation for the allocation of Shared Address Space is
as address space for CGNs; the use and impact of CGNs has been
previously described in [RFC6269] and [NAT444-IMPACTS]. Some
of the services adversely impacted by CGNs are as follows:
Console gaming -- some games fail when two subscribers using the
same outside public IPv4 address try to connect to each other.
Video streaming -- performance is impacted when using one of
several popular video-streaming technologies to deliver multiple
video streams to users behind particular CPE routers.
Peer-to-peer -- some peer-to-peer applications cannot seed
content due to the inability to open incoming ports through the
CGN. Likewise, some SIP client implementations cannot receive
incoming calls unless they first initiate outgoing traffic or
open an incoming port through the CGN using the Port Control
Protocol (PCP) [PCP-BASE] or a similar mechanism.
Geo-location -- geo-location systems identify the location of the
CGN server, not the end host.
Simultaneous logins -- some websites (particularly banking and
social-networking websites) restrict the number of simultaneous
logins per outside public IPv4 address.
6to4 -- 6to4 requires globally reachable addresses and will not
work in networks that employ addresses with limited topological
span, such as those employing CGNs.
Edit:
Based on your comments, I see that you are confused. You think the addressing looks like this:
192.168.1.1[LAN-Your Router-WAN]83.79.34.21<-->10.255.195.1[ISP router]Internet
In reality, it looks something like this:
192.168.1.1[LAN-Your Router-WAN]10.255.195.2<-->10.255.195.1[ISP router]83.79.34.21<-->Internet
When you go to a web site that reports your public address, it only sees the ISP public address 83.79.34.21 since the private addresses assigned to your router cannot be routed on the public Internet. That public address is not on your router, it is on an ISP router. All your traffic gets translated on your router between two private address blocks, and it gets translated again on the ISP router from private to public addresses. That double NAT may cause problems for you, depending on what you try to do.
